A207820 Let A = A025584. a(n) is the smallest A(m) such that the interval (A(m)*n, A(m+1)*n) contains no primes from A.

2, 2, 2, 1783, 967, 1663, 3187, 4813, 13873, 20347, 1783, 2617, 27743, 14533, 54829, 71143, 66169, 46687, 44119, 57787, 79609, 552883, 21397, 297079, 1187107, 89017, 798697, 285763, 761377, 2660587, 812047, 1463257, 2795059, 2816239, 2676727, 3069607, 2500297

Offset

1,1

Comments

Conjecture. For n>=3, every a(n) is the lesser of a pair of cousin primes p and p+4, cf. A023200.

The limit of a(n) as n goes to infinity is infinity.

Links

Table of n, a(n) for n=1..37.

Mathematica

Table[aPrime[[NestWhile[#1+1&, 1, !(nextAPrime[n aPrime[[#1]]]>n aPrime[[#1+1]])&]]], {n, 2, 20}]

Prog

(PARI) is_a025584(x) = isprime(x) && !isprime(x-2)
a025584_next(n) = {local(p); p=n+1; while(!is_a025584(p), p=p+1); p}
no_a025584(a, b) = {local(x, r); r=1; for(x=a+1, b-1, if(is_a025584(x), r=0)); r}
a207820(n) = {local(r, rp); rp=2; r=3; while(!no_a025584(n*rp, n*r), rp=r; r=a025584_next(r)); rp} \\ Michael B. Porter, Jan 20 2013

Crossrefs

Cf. A025584, A023200, A195325.

Sequence in context: A324302 A216668 A057330 * A186069 A280842 A244442

Adjacent sequences: A207817 A207818 A207819 * A207821 A207822 A207823

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 10 2013

Extensions

a(21)-a(37) from Michael B. Porter, Jan 20 2013

Status

approved